95
95
Oct 23, 2018
10/18
Oct 23, 2018
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In this paper, we derive and prove, by means of Binomial theorem and Faulhaber's formula, the following identity between m -order polynomials in T ∑ l k=1 ∑ j m=0 A m,j k j (T-k) j = ∑ m k=0 (-1) m-k U m (l,k) ∙ T k = T 2m+1
Topics: Faulhaber's formula, Faulhaber's theorem, Binomial Theorem, Binomial coefficient, Binomial...
68
68
May 1, 2017
05/17
May 1, 2017
by
Kolosov Petro
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Calculating the value of C k ∈ { 1 , ∞ } class of smoothness real-valued function's derivative in point of R + in radius of convergence of its Taylor polynomial (or series), applying an analog of Newton's binomial theorem and q -difference operator. ( P , q ) -power difference introduced in section 5. Additionally, by means of Newton's interpolation formula, the discrete analog of Taylor series, interpolation using q -difference and p , q -power difference is shown. ARXIV : 1705.02516 DOI :...
Topics: Mathematics, Quantum calculus, Quantum algebra, Power quantum calculus, Quantum difference,...
107
107
Apr 30, 2017
04/17
Apr 30, 2017
by
Kolosov Petro
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The main aim of this paper to establish the relations between forward, backward and central finite and divided differences (that is discrete analog ofthe derivative) and partial and ordinary high-order derivatives of polynomials. DOI : 10.6084/m9.figshare.4955384 , 10.17605/OSF.IO/DQNCJ ORCID: https://orcid.org/0000-0002-6544-8880 Personal Website: https://kolosovpetro.github.io/ Keywords : Finite difference, Derivative, Divided difference, Ordinary differential equation, Partial...
Topics: Mathematics, Finite difference, Derivative, Divided difference, Ordinary differential equation,...
70
70
Apr 30, 2017
04/17
Apr 30, 2017
by
Kolosov Petro
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Abstract : In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence A287326 in OEIS. The main property of A287326 that it returns a perfect cube n as sum of n-th row terms over k, 0
Topics: Series Representation, Power function, monomial, Binomial Theorem, Multinomial theorem, Worpitzky...
101
101
Jul 8, 2016
07/16
Jul 8, 2016
by
Kolosov Petro
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Abstract : In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence A287326 in OEIS. The main property of A287326 that it returns a perfect cube n as sum of n-th row terms over k, 0
Topics: Series Representation, Power function, monomial, Binomial Theorem, Multinomial theorem, Worpitzky...
73
73
Apr 7, 2016
04/16
Apr 7, 2016
by
Kolosov Petro
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Abstract : In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence A287326 in OEIS. The main property of A287326 that it returns a perfect cube n as sum of n-th row terms over k, 0
Topics: Series Representation, Power function, monomial, Binomial Theorem, Multinomial theorem, Worpitzky...
92
92
Mar 16, 2016
03/16
Mar 16, 2016
by
Kolosov Petro
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Abstract : In this paper we discuss a problem of generalization of binomial distributed triangle, that is sequence A287326 in OEIS. The main property of A287326 that it returns a perfect cube n as sum of n-th row terms over k, 0
Topics: Series Representation, Power function, monomial, Binomial Theorem, Multinomial theorem, Worpitzky...
